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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">finance</journal-id><journal-title-group><journal-title xml:lang="ru">Финансы: теория и практика/Finance: Theory and Practice</journal-title><trans-title-group xml:lang="en"><trans-title>Finance: Theory and Practice</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2587-5671</issn><issn pub-type="epub">2587-7089</issn><publisher><publisher-name>Financial University under The Government of Russian Federation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26794/2587-5671-2026-30-4-19-37</article-id><article-id custom-type="elpub" pub-id-type="custom">finance-4550</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФОНДОВЫЕ РЫНКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>STOCK MARKETS</subject></subj-group></article-categories><title-group><article-title>Построение динамических портфельных моделей высокого порядка на основе VAR-ICA-MGARCH</article-title><trans-title-group xml:lang="en"><trans-title>Construction of High-order Dynamic Portfolio Models Based on VAR-ICA-MGARCH</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-2478-0307</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Михайлов</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Mikhaylov</surname><given-names>A. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексей Юрьевич Михайлов — кандидат экономических наук, доцент, кафедра финансовых технологий; научный сотрудник</p><p>Москва</p><p>Баку</p></bio><bio xml:lang="en"><p>Alexey Yu. Mikhaylov — Cand. Sci. (Econ.), Assoc. Prof., Department of Financial Technologies; researcher</p><p>Moscow</p><p>Baku</p></bio><email xlink:type="simple">alexeyfa@ya.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5237-5347</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Юсиф</surname><given-names>Н. Б.A.</given-names></name><name name-style="western" xml:lang="en"><surname>Yousif</surname><given-names>N. B.A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Нагва Б. А. Юсиф — PhD, доцент, кафедра социологии</p><p>Аджман</p></bio><bio xml:lang="en"><p>Nagwa B. A. Yousif — PhD, Assoc. Prof., Department of Sociology</p><p>Ajman</p></bio><email xlink:type="simple">nagway37@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9971-6169</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сотсков</surname><given-names>Ю. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Sotskov</surname><given-names>Yu. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Юрий Николаевич Сотсков — доктор экономических наук, профессор</p><p>Минск</p></bio><bio xml:lang="en"><p>Yury N. Sotskov — Dr. Sci. (Econ.), Prof.</p><p>Minsk</p></bio><email xlink:type="simple">sotskov48@mail.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5102-676X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хомякова</surname><given-names>Л. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Khomyakova</surname><given-names>L. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Любовь Игоревна Хомякова — кандидат экономических наук, доцент кафедры международной экономики</p><p>Москва</p></bio><bio xml:lang="en"><p>Lyubov I. Khomyakova — Cand. Sci. (Econ.), Assoc. Prof., Department of International Economics</p><p>Moscow</p></bio><email xlink:type="simple">lihomyakova@fa.ru</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Финансовый университет при Правительстве Российской Федерации; Бакинский Евразийский университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Financial University under the Government of the Russian Federation; Baku Eurasian University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Колледж гуманитарных наук, Аджманский университет; Исследовательский центр гуманитарных и социальных наук (HSSRC), Аджманский университет</institution><country>Объединенные Арабские Эмираты</country></aff><aff xml:lang="en"><institution>College of Humanities and Sciences, Ajman University; Humanities and Social Sciences Research Centre (HSSRC), Ajman University</institution><country>United Arab Emirates</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Объединенный институт проблем информатики, Национальная академия наук Беларуси</institution><country>Беларусь</country></aff><aff xml:lang="en"><institution>United Institute of Informatics Problems, National Academy of Sciences of Belarus</institution><country>Belarus</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>Финансовый университет при Правительстве Российской Федерации</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Financial University under the Government of the Russian Federation</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>18</day><month>08</month><year>2026</year></pub-date><volume>30</volume><issue>4</issue><fpage>19</fpage><lpage>37</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Михайлов А.Ю., Юсиф Н.Б., Сотсков Ю.Н., Хомякова Л.И., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Михайлов А.Ю., Юсиф Н.Б., Сотсков Ю.Н., Хомякова Л.И.</copyright-holder><copyright-holder xml:lang="en">Mikhaylov A.Y., Yousif N.B., Sotskov Y.N., Khomyakova L.I.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://financetp.fa.ru/jour/article/view/4550">https://financetp.fa.ru/jour/article/view/4550</self-uri><abstract><p>Целью исследования является доказательство того, что динамические портфели способны эффективно отражать временную динамику текущих рисков более высокого порядка, обеспечивая при этом более высокую надежность и стабильность по сравнению с традиционными портфелями. Предметом является экономическая асимметрия в портфельных моделях, которая возникает, когда разные участники обладают знаниями о рыночных условиях и показателях активов. В условиях, когда традиционные портфели демонстрируют низкие показатели доходности из-за ярко выраженных пиков и резких спадов доходности финансовых активов, а также из-за их неспособности учитывать динамические изменения финансовых рисков, данное исследование включает в традиционные портфели краткосрочные риски более высокого порядка, чтобы смягчить последствия отклонений от нормального распределения. Методология основана на концепции множественных финансовых временных рядов и модели VAR-ICA-MGARCH. Эта модель эффективно фиксирует условное среднее, ковариационную матрицу, матрицу взаимной асимметрии и матрицу взаимного эксцесса, тем самым характеризуя временные изменения в моменты более высокого порядка. Из-за присущих задачам оптимизации динамического портфеля нелинейностей мы используем генетический алгоритм для решения модели динамического портфеля. Результаты исследования показывают, что динамические портфели способны эффективно отражать временную динамику текущих рисков более высокого порядка, обеспечивая при этом более высокую надежность и стабильность по сравнению с традиционными портфелями, даже когда они подвержены таким сложным рискам. Практическая значимость исследования заключается в определении изменяющихся во времени весовых коэффициентов портфеля и проведении как имитационных экспериментов, так и эмпирического анализа.</p></abstract><trans-abstract xml:lang="en"><p>The aim of the study is to prove that dynamic portfolios can effectively reflect the temporal dynamics of current risks of a higher order, providing greater reliability and stability compared to traditional portfolios. The subject is the economic imbalance in portfolio models, which occurs when different participants have different level of knowledge about market conditions and the performance of assets. In an environment where traditional portfolios have shown low returns due to the pronounced peaks and sharp declines in financial asset returns, as well as their inability to account for dynamic changes in financial risks. This study incorporates higher-order short-term risks into traditional portfolios in order to mitigate the effects of deviations from the normal distribution. The methodology is based on the concept of multiple financial time series and the VAR-ICA-GARCH model. This model effectively captures the conditional mean, the covariance matrix, the mutual asymmetry matrix, and the mutual kurtosis matrix, thereby characterizing temporal changes at higher-order moments. Due to the inherent nonlinearities of dynamic portfolio optimization tasks, we use a genetic algorithm to solve the dynamic portfolio model. The results of the study show that dynamic portfolios can effectively reflect the changing dynamics of current higher-order risks, while providing greater reliability and stability than traditional portfolios. Even when exposed to such complex risks, dynamic portfolios perform better. The practical significance of this research lies in determining the time-varying weighting coefficients for the portfolio and conducting both simulation experiments and empirical analysis.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>ИИ</kwd><kwd>динамический инвестиционный портфель высокого порядка</kwd><kwd>генетический алгоритм</kwd><kwd>модель VAR-ICA-MGARCH</kwd><kwd>функция полезности CARA</kwd></kwd-group><kwd-group xml:lang="en"><kwd>AI</kwd><kwd>high-order dynamic investment portfolio</kwd><kwd>genetic algorithm</kwd><kwd>VAR-ICA-MGARCHSK model</kwd><kwd>CARA utility function</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа Ю. Н. Сотскова (разделы 1–2) выполнена при поддержке Белорусского республиканского фонда фундаментальных исследований, грант Ф26КИ-009. Объединенный институт проблем информатики, Национальная академия наук Беларуси, Минск, Беларусь. Работа Л. И. Хомяковой (разделы 3–4) подготовлена на основе результатов исследований, проведенных за счет бюджетных средств по государственному заданию Финансового университета. Финансовый университет при Правительстве Российской Федерации, Москва, Российская Федерация. Авторы благодарят Дарона Асемоглу за исследования в области искусственного интеллекта.</funding-statement><funding-statement xml:lang="en">The work of Yu. N. Sotskov (sections 1–2) was supported by the Byelorussian Republican Foundation of Fundamental Research, grant Ф26КИ-009. United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus. The work of Lu. I. Khomyakova (sections 3–4) is based on the results of research conducted at the expense of budgetary funds under the state assignment of the Financial University. Financial University under the Government of the Russian Federation, Moscow, Russian Federation. 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